Competitive Control
This work addresses control system design for scenarios where controllers must operate online without foresight, offering a novel competitive analysis approach that could benefit robotics, autonomous systems, and other real-time control applications.
The paper tackles the problem of designing online controllers that compete against clairvoyant offline optimal controllers, using competitive ratio as a performance metric. It derives a computationally efficient state-space controller with optimal competitive ratio for linear systems and extends it to nonlinear systems via Model Predictive Control (MPC), showing significant performance improvements over standard H₂ and H∞ controllers in numerical experiments.
We consider control from the perspective of competitive analysis. Unlike much prior work on learning-based control, which focuses on minimizing regret against the best controller selected in hindsight from some specific class, we focus on designing an online controller which competes against a clairvoyant offline optimal controller. A natural performance metric in this setting is competitive ratio, which is the ratio between the cost incurred by the online controller and the cost incurred by the offline optimal controller. Using operator-theoretic techniques from robust control, we derive a computationally efficient state-space description of the the controller with optimal competitive ratio in both finite-horizon and infinite-horizon settings. We extend competitive control to nonlinear systems using Model Predictive Control (MPC) and present numerical experiments which show that our competitive controller can significantly outperform standard $H_2$ and $H_{\infty}$ controllers in the MPC setting.